1. Field of the Invention
The present invention relates to digital filters. More specifically, the invention relates to a method and apparatus for modeling and synthesizing the phase component in digital filters.
2. Description of Related Art
Digital filters are used to model audio and video signals. Digital signals represented in the frequency domain as complex numbers have a phase component and a magnitude component. For instance, transfer functions describing the effect of sound travelling through space may be represented by a set of complex values that contains magnitude components and phase components. The magnitude and phase components of an audio transfer function are measured and stored in a memory. Typically, a digital filter accesses the phase component and magnitude component of a sound source from memory in order to resynthesize or model a particular sound effect.
Several techniques were used to reduce the amount of space required to store the phase component and magnitude component data. One technique reduced the magnitude components using an algorithm, such as principal component analysis (PCA) before storing the components in memory. The phase components of the digital signals were discarded and not stored in memory.
When reconstructing the digital filter, a phase component from a model was substituted for the original phase component. Two models used for modeling phase components were the linear phase model and the minimum phase model. According to the linear phase model, the phase increases linearly as the frequency increases. Under the minimum phase model, the phases are calculated in the time domain so that the filter is as short as possible. One advantage of the minimum phase model is that the filter is shorter and thus easier to compute.
Both the linear phase and minimum phase models operated on the erroneous assumption that eliminating the authentic phase component of a filter did not affect the sound quality of an audio signal. This assumption is not supported by the following facts. There is a delay between the time a sound signal enters a filter and the time the transformed sound signal leaves the filter. This delay varies with the frequency of the sound signal. But when one restores the information stored in the phase component using the linear or the minimum phase models, the frequency-dependent-delay information is lost. Thus, one of the drawbacks of using the linear or minimum phase models is the loss of the absolute time delay of the filter.
In particular, when using matched sets of filters, such as those used to represent head-related transforms, one loses the frequency-dependent Interaural Time Delay (ITD). This causes a decrease in the sound quality obtained from the filters. In order to restore the original sound quality to the filters, one must independently restore the ITD. Thus, removing or modeling the phase component achieves a sound quality inferior to using the original phase component to construct the digital filter.